Phase-Mediated Attractor Dynamics in Millisecond Pulsar Timing Residuals

We present a phase-space analysis of NANOGrav 15-year millisecond pulsar timing residuals using \emph{Phase-Mediated Attractor Dynamics} (PMAD). By constructing cosine-delta sequences from residual state embeddings and projecting onto stiff (low-variance) axes, we reveal consistent low-dimensional manifolds underlying the stochastic residuals. Across multiple pulsars, we find a robust \emph{dimensional collapse} onto 5--6 stiff axes, with intermittent bursty trajectories reminiscent of chaotic attractors. Angular Lyapunov proxies and basin-depth measures quantify local phase contraction and metastable organization, suggesting universal phase-space scaffolds beyond individual pulsar red noise. The pipeline and datasets are released for reproducibility.